Back up your iPhone properly.
I switched on iCloud backup rather than local backup for the old iPhone. Most apps I use have their own iCloud, Dropbox or other backup service so I didn’t bother with them. I was not going to lose any data, I knew it. I just didn't appreciate how much else gets backed up when you backup your phone directly to your computer through iTunes.
By connecting my phone to my iMac I would've got all my apps back, plus all their settings. In an effort to save space (because iCloud is limited in its free incarnation to 5GB), the iCloud-only backup of an iPhone doesn't remember all that minutia, it just puts your purchased apps back on in the order they are restored.
The bottom line here: back up your iPhone and iPad to your Mac through iTunes, rather than an iCloud backup, and do it regularly -- if you want to be able to restore the your iOS device exactly as it was when you replace it. The iCloud backup is good in its way, particularly for people who don't tie their device to a Mac or Windows PC, but it is not as complete. High scores in games not using Game Center, for example, aren't saved -- you can pretend it won't bother you, but you know it will.